Primary versus ternary adsorption of proteins onto PEG brushes

Polyethylene glycol (PEG) brushes are used to reduce protein adsorption at surfaces. Their design needs to allow for two leading adsorption modes at the brush-coated surface. One is primary adsorption at the surface itself. The second is ternary adsorption within the brush as a result of weak PEG-protein attraction. We present a scaling theory of the equilibrium adsorption isotherms allowing for concurrent primary and ternary adsorption. The analysis concerns the weak adsorption limit when individual PEG chains do not bind proteins. It also addresses two issues of special relevance to brushes of short PEGs: the consequences of large proteins at the surface protruding out of a shallow brush and the possibility of marginal solvent conditions leading to mean-field behavior. The simple expressions for the adsorption isotherms are in semiquantitative agreement with experiments.